Preheat the oven to 425°F (220°C). If time allows, let the salmon sit at room temperature for a few minutes for even cooking.
Pat the salmon dry with paper towels and season both sides generously with salt and pepper.
Place an oven-safe skillet over medium-high heat for 3–4 minutes, until drops of water sizzle and bead on the surface.
Add 2 tablespoons oil to the hot skillet and swirl to coat. The oil may begin to smoke lightly.
Gently place the salmon fillets in the skillet, meat side down, without crowding; if using skin-on fillets, place them skin side up so the meat contacts the pan.
Increase the heat to high and sear the fillets undisturbed for 2–3 minutes, until a golden brown crust forms at the edge where the fish touches the pan.
Do not flip the fillets; transfer the skillet to the preheated oven and roast for 6–10 minutes depending on thickness and desired doneness (about 7–8 minutes for a 1-inch-thick fillet).
Carefully remove the hot skillet from the oven with an oven mitt, then lift the fillets out with tongs or a fish spatula, plating them crust-side up.
Serve immediately; note that the fillets will continue to cook if left in the hot skillet.